Glasnik matematički, Vol. 47 No. 2, 2012.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.47.2.14
Linear independence and sets of uniqueness
Hrvoje Šikić
; Department of Mathematics, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia
Ivana Slamić
orcid.org/0000-0002-3284-8052
; Department of Mathematics, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia
Sažetak
Consider the Bessel system of integer translates {ψk} of a square integrable function ψ. We show that lp-linear independence of {ψk} is equivalent to periodization function pψ(ξ)=∑k Z|(ξ+k)|2 vanishing almost everywhere on a set which is an lp-set of uniqueness, where 1≤ p≤ 2. General result, concerning no restriction on Bessel systems is then proved for the case p=1.
Ključne riječi
Integer translates; l^p-linear independence; sets of uniqueness
Hrčak ID:
93956
URI
Datum izdavanja:
19.12.2012.
Posjeta: 1.301 *